From: Matthew Moss Date: 2008-10-28T06:01:53+09:00 Subject: Re: float equality >>> x = 0.999... >>> 10x = 9.999... >>> (10x - x) = 9.999... - 0.999... >>> 9x = 9 >>> x = 1 >> >> While your answer is correct, you cannot subtract infinities as shown >> in your proof. Look at this: >> >> x == 1 - 1 + 1 - 1 + 1 - 1 + 1 - ... >> x == 1 - 1 + 1 - 1 + 1 - 1 + ... >> ---------------------------------------- >> 2x == 1 + 0 + 0 + 0 + 0 + 0 + 0 + ... >> x == 0.5 >> >> Does x == 0.5? No, because x was never a number in the first place >> because the given series does not converge. Your proof appears to >> work because you've already assumed 0.99999... converges, but that is >> what you are trying to prove. > > > But 0.999... does converge, while 1 - 1 + 1 - 1 +... does not. On re-reading, I see that you weren't so much questioning whether 0.999... converges, but that my proof uses circular reasoning. Yeah, I suppose that's correct. Still, 0.999... does converge and is 1. Nyah! :p I just don't remember the better proof I once knew.